Q1
Is it possible to prove a unique continuation result similar to those proved in [1]}, [2]} for the system (REF )?
Q2
As a consequence of the unique continuation of solutions proved in [1]}, [2]}, in [2]} was shown that the periodic CH equation does not have non-trivial compactly supported solutions. By a periodic and compactly supported solution we mean a periodic solution such that the support of its restriction to \([0,1)\)  is compact. As far as the author knows, the following question has not been addressed so far for the CH2 system: Can the periodic solutions of (REF ) be compactly supported?
Q3
Is it possible to conclude that the system (REF ) does not have non-trivial compactly supported solutions defined on suitable Banach spaces of functions defined on \(\mathbb {R}\) , similarly as proved in [2]}?

